Steven Gerrard will surely be determined to keep the midfielder at Rangers, however.
Central midfield is clearly an area where Hammers boss David Moyes will be looking to strengthen at the London Stadium this summer.
Money is fairly tight at West Ham, however. So Moyes will have to be sensible with his player recruitment this summer.
And it seems as though the Scot has his eye on a potential bargain.
Brentford, Watford, Arsenal and Everton are also thought to be keen on signing the 34-capped Finland International (Give Me Sport).
Kamara is a tough-tackling, defensive midfielder.
In 28 Scottish Premiership appearances for Rangers last season, the 25-year-old averaged one tackle and one interception per game. He made 65.9 passes per match on average during those outings and recorded a mightily impressive completion rate of 90.5%